In this chapter, we present the microscopic (Langevin equation) and macroscopic (Fokker–Planck equation) descriptions of Brownian motion and confirm their consistency. Furthermore, we provide a detailed introduction to the Poisson process, which forms the foundation of chemical reactions. Subsequently, we introduce the chemical Langevin equation and its corresponding Fokker–Planck equation, which are utilized in modeling molecular number fluctuations in chemical reactions. We also explain stochastic differential equations with both the Ito and Stratonovich types of integrals. Exploring mechanisms arising from the presence of noise, we discuss noise-induced transitions and attractor selection and adaptation in dynamical systems, elucidating their functional significance in cells. Finally, as an advanced topic, we introduce adiabatic elimination in stochastic systems.